Fig 1.
Illustration of the effect of stiffening the ankle (in orange) (e.g., by co-activation) on body movement induced by a backward translation versus toe-up rotation of the platform.
A stiff ankle will help to keep the body upright in response to translational perturbations by resisting movement of the body with respect to the feet whereas it will lead to additional body tilt in response to rotational perturbations by coupling body to platform movement. Backward translational perturbations will require balance correcting activity of the plantar flexors to counteract forward body tilt whereas rotational toe-up perturbations will require balance correcting activity of the tibialis anterior to counteract backward body tilt.
Table 1.
Demographic data of participants (mean and standard deviations).
Fig 2.
Experimental set-up and perturbation profiles.
a) Caren platform for combined translational and rotational perturbations and b) platform kinematics and exemplar reactive balance responses for a typically developing child for the different perturbation levels (L1-L4). One perturbation involved simultaneous translation and rotation of the platform. Platform displacement increased from L2 to L3, while platform velocity and acceleration increased with every level. Row 1: Platform kinematics: displacement, velocity, and acceleration of a point on the platform between the ankles; row 2: Angular displacement, velocity, and acceleration; row 3: center of mass kinematics (anterior-posterior direction) relative to the ankle; row 4: ankle kinematics; row 5: muscle responses. Vertical grey line indicates platform onset LG = lateral gastrocnemius; SOL = soleus; TA = tibialis anterior.
Fig 3.
Representative examples for center of mass movement, ankle kinematic, and muscle activity for perturbation level 2 in time bins (zones) for a child with cerebral palsy (left) and typically developing child (right). Both children had moderate co-activation (exemplar trajectories for children with high/low co-activation can be found in Figs B and C in S1 Text).
Row 1–3: Center of mass kinematics (displacement, velocity, and acceleration) as a function of time with indication of time bins (dotted lines, colored boxes) and average trajectories (black). Time bin 1 (Z1) in blue, time bin 2 (Z2) in yellow, and time bin 3 (Z3) in red; Row 4–6: Ankle angle kinematics (angle, velocity, and acceleration) as a function of time with indication of time bins and average trajectories. Row 7–9: Muscle activations as a function of time with indications of time bins and average muscle activity. Light gray traces are separate trials of one subject. The bars represent the average for each time bin for the corresponding (black) trace (average over trials) on the left.
Fig 4.
a) Graphical representation of the (extended) sensorimotor response model. Measured muscle activity (black) is reconstructed (red) using delayed feedback of CoM acceleration, velocity, displacement, and stiction (for plantar flexors only) along a balance-correcting pathway (green) and antagonistic pathway (orange; sensitive to CoM movement in the opposite direction). CoM acceleration, velocity, position, and stiction are multiplied by subject specific feedback gains (balance correcting: ka, kv, kd, ks; antagonistic pathway: ka’, kv’, kd’). Note the opposite sign of the CoM kinematics in the balance correcting (green) and antagonistic pathways (orange) of the plantar flexors (top row) and tibialis anterior (bottom row). In the extended model, both pathways are used (balance correcting and antagonistic gains), while in the simple model only the gains of the balance correcting pathway are used. b) Exemplar cases with the extended sensorimotor response model for one child with cerebral palsy (left) and one typically developing child (right) with average co-activation for perturbation level 2. Exemplar cases for children with high and low co-activation are presented in Fig E in S1 Text. Top row: center of mass kinematics; second row: measured (black) and reconstructed (red) muscle activity signals with balance correcting contribution in green and antagonistic contribution in orange; third row: balance correcting gains; bottom row: antagonistic gains (i.e., prime gains). Grey line indicated onset of perturbation. LG = lateral gastrocnemius; SOL = soleus; TA = tibialis anterior.
Fig 5.
Average normalized EMG for three time bins (Z1-Z3) for all muscles and all levels.
Children with cerebral palsy (CP) in orange, typically developing (TD) children in blue. Group average for children with cerebral palsy in red, group average for typically developing children in dark blue. Significant interaction effects after Bonferroni-Holm correction between time bin and group (p < 0.05) are indicated with a diamond.
Fig 6.
Average center of mass (a) and ankle kinematics (b) for three time bins (Z1-Z3) for all levels.
Children with cerebral palsy (CP) in orange, typically developing (TD) children in blue. Group average for children with cerebral palsy in red, group average for typically developing children in dark blue. Significant interaction effects after Bonferroni-Holm correction between time bin and group (p < 0.05) are indicated with a diamond.
Fig 7.
Co-contraction index for perturbation onset until 400ms after perturbation onset.
Children with cerebral palsy (CP) in orange, typically developing (TD) children in blue. Boxplots in black indicate median and interquartile range and dots represent individual scores. Groups are significantly different across all levels for all muscle pairs. LG = lateral gastrocnemius; MG = medial gastrocnemius; SOL = soleus; TA = tibialis anterior.
Fig 8.
Goodness of fit for the extended sensorimotor response model and reduction in cost for the extended versus simple sensorimotor response model.
a) Goodness of fit values and error scores across all levels for all muscles for the extended (with antagonistic pathways) sensorimotor response model. Standard deviations are indicated in black. r2 = r squared; VAF = variance accounted for; RMSE = root mean square error. b) Improvement in cost (%) when using the extended versus simple (no antagonistic pathways) sensorimotor response model for all muscles. The cost is the squared difference between measured and reconstructed EMG. Boxplots in black indicate median and interquartile range, dots represent individual scores. Significant differences between groups (CP vs. TD) are indicated with a star and p-values. LG = lateral gastrocnemius; MG = medial gastrocnemius; SOL = soleus; TA = tibialis anterior. Children with cerebral palsy (CP) in orange, typically developing (TD) children in blue.
Fig 9.
Center of mass feedback gains of children with cerebral palsy and typically developing children.
a) Lateral gastrocnemius. b) Tibialis Anterior. Differences between children with CP and TD children were larger for lateral gastrocnemius than for soleus and medial gastrocnemius, therefore results for lateral gastrocnemius are shown in the main figure. Figures for medial gastrocnemius and soleus can be found in Fig F in S1 Text. Upper row: balance correcting pathway gains, bottom row: antagonistic pathway gains. L1-L4: Level 1 to level 4. Boxplots in black indicate mean and interquartile ranges and dots represent individual scores. Children with cerebral palsy (CP) in orange, typically developing (TD) children in blue. Significant differences between groups are indicated with a star after Bonferroni-Holm correction. A star between brackets indicates significant effects that did not survive the Bonferroni-Holm correction.